Multi-agricultural Machinery Collaborative Task Assignment Based on
Improved Genetic Hybrid Optimization Algorithm
Haohao Du , Huicheng Lai, Guxue Gao, Xiaopeng Wen,
Yifei Li, Haidong Wang, Guo Zhang
1
College of Information Science and Engineering, Xinjiang University, Urumqi 830017, China
2
Key Laboratory of Signal Detection and Processing, Xinjiang University, Urumqi 830017,
China
Correspondence: Huicheng Lai. Email: lai@xju.edu.cn
Abstract: Agricultural machinery collaboration technology is crucial in improving the
efficiency of agricultural machinery utilisation and enhancing the benefits of large-scale
production of machinery fleets. To address the challenges of delayed scheduling
information, heavy reliance on manual labour, and low operational efficiency in traditional
large-scale agricultural machinery operations, this study proposes a method for
multi-agricultural machinery collaborative task assignment based on an improved genetic
hybrid optimisation algorithm. The proposed method establishes a multi-agricultural
machinery task allocation model by combining the path pre-planning of a simulated
annealing algorithm and the static task allocation of a genetic algorithm. By sequentially
fusing these two algorithms, their respective shortcomings can be overcome, and their
advantages in global and local search can be utilised. Consequently, the search capability
of the population is enhanced, leading to the discovery of more optimal solutions. Then,
an adaptive crossover operator is constructed according to the task assignment model,
considering the capacity, path cost, and time of agricultural machinery; two-segment
coding and multi-population adaptive mutation are used to assign tasks to improve the
diversity of the population and enhance the exploration ability of the population; and to
improve the global optimisation ability of the hybrid algorithm, a 2-Opt local optimisation
operator and an Circle modification algorithm are introduced. Finally, simulation
experiments were conducted in MATLAB to evaluate the performance of the
multi-agricultural machinery collaborative task assignment based on the improved genetic
hybrid algorithm. The algorithm's capabilities were assessed through comparative
analysis in the simulation trials. The results demonstrate that the developed hybrid
algorithm can effectively reduce path costs, and the efficiency of the assignment
outcomes surpasses that of the classical genetic algorithm. This approach proves
particularly suitable for addressing large-scale task allocation problems.
Keywords: Agricultural machinery; Task assignment; Genetic algorithm; Adaptive crossover
operator; Adaptive mutation operator
1. Introduction
With the continuous advancement of science and technology, our country's mechanisation level
in agriculture has significantly improved. Automation technology has become a key area in the
development of modern agriculture. Agricultural machinery automatic navigation technology is
crucial for implementing precision agriculture [1] and enables efficient and accurate agricultural
machinery operations. Integrating farm machinery and information technology has become
inevitable in developing modern agricultural machinery in China. Leveraging information
technology to promote agricultural machinery development can maximise information
technology's guiding role, enhance agricultural production efficiency, and hold significant
importance for promoting the high-quality and efficient development of agricultural machinery in

our country [2]. Smart agriculture plays a crucial role in economic development, and a range of
innovations are already being applied in developed countries that enable farmers to reduce
resource consumption and increase agricultural production effectively[3]. [4]Research has
explored the master-slave navigation system of two agricultural machines, and experimental
results demonstrate that these two agricultural machines can collaborate safely, with a 95.1%
increase in efficiency compared to traditional single-machine operations. Additionally,[5]proposed
a novel agricultural master-slave navigation system where the slave machine tracks the operation
of the master machine, achieving preliminary collaborative navigation.
Multi-machine collaboration technology in agricultural machinery is crucial for enhancing the
efficiency of machinery utilisation and improving the benefits of large-scale production of
machinery fleets. Task allocation is also a significant evaluation metric for collaborative
operations within agricultural machinery fleets. The challenge lies in allocating each task to the
most suitable agricultural machinery unit before commencing operations, thereby maximising the
overall benefits of the machinery fleet. Multi-machine collaborative task allocation has been
extensively researched in logistics distribution, drones, and robotics. The integration of robotics
and automation technology has significantly transformed the landscape of agriculture. The
emergence of automated agriculture and the utilisation of robotics and sensors[6-9]aim to
accomplish agricultural tasks more efficiently, thereby increasing production efficiency, reducing
manual operations, cutting labour costs, and executing functions like field management, crop
cultivation, and harvesting with greater precision. The primary goal is to address issues related to
agricultural machinery's production efficiency and crop yield. Furthermore, unmanned driving
technology has led to the development of high-precision autonomous driving tractors, which have
applications in various agricultural activities such as ploughing and harvesting[10-11].Rational
task allocation in multi-machine operations can accelerate the execution speed of fleet tasks and
reduce system consumption[12], primarily aimed at minimising production costs.[13]introduced a
solution utilising a dual-layer distributed Multi-Agent System (MAS) framework. They employed
an iterative auction approach at the production planning layer and a distributed Hungarian method
at the scheduling layer to address the multi-robot task allocation problem.[14]introduced a hybrid
particle swarm optimisation and simulated annealing algorithm to find high-quality workshop
scheduling solutions within reasonable computational time.[15]proposed a distributed auction
algorithm based on the distance between robots and target tasks and the matching degree between
robot capabilities and functions. They established a multi-robot collaborative task allocation
model in a heterogeneous environment, effectively addressing the task allocation problem among
heterogeneous robots. To manage the scheduling of multi-robot collaborative navigation task
planning,a method based on ant colony algorithms was proposed for multi-robot collective
navigation operations in agricultural fields [16]. Subsequently, a remote management platform for
multi-robot coordinated navigation operations was designed and developed[17]. This platform can
monitor real-time trajectories and operational information of multi-robot collaborative navigation
operations and facilitate remote scheduling and management, thereby preliminary meeting the
requirements of multi-robot collective navigation operations and reducing costs.[18]developed a
multi-UAV task allocation algorithm based on an improved particle swarm optimisation algorithm.
This algorithm builds upon the traditional particle swarm optimisation by introducing partial
matching crossover and second-order swap mutation. These enhancements effectively enhance the
efficiency of UAV task allocation in maritime environments and optimise navigation paths.

[19]presented a multi-UAV integrated scheduling optimisation method that divides the problem
into task allocation and individual UAV scheduling stages. This approach achieves task allocation
among multiple UAVs.[20]proposed a solution to the task allocation problem in multi-machine
collaborative agricultural machinery operations. They devised a method based on the
multi-mutated grouping genetic algorithm for assigning static tasks when similar farm machines
must work together. They constructed the multi-mutated grouping genetic algorithm and designed
a two-stage encoding, grouping crossover operator, and multiple mutation operators. They
established a static task allocation model for multi-machine collaborative agricultural machinery
operations, meeting the requirements of practical task allocation in collaborative scenarios. The
research was done on multi-agricultural machinery cooperative task allocation based on an
improved ant colony algorithm in agricultural field environments [21]. This was done to help
manage operations involving multiple machines working together. This study laid the foundation
for addressing task scheduling and management in complex agricultural operational environments
that involve multi-machine collaboration.
While significant progress has been made by scholars both domestically and internationally in
the field of multi-machine collaborative task allocation, there are still several limitations that need
to be addressed. Firstly, a large portion of research has been applied to areas such as multi-robot
systems,multi-UAVs, and multi-autonomous underwater vehicles, with only a few studies
focusing on integrating agricultural machinery into the context of farming applications. Secondly,
in solving task allocation problems using various algorithms, past research has mainly
concentrated on optimising the algorithms' performance, such as improving efficiency and
addressing issues related to local optima [22-23]. However, task allocation is a multi-constrained
optimisation problem in practical agricultural field operations. Beyond minimising path costs,
other factors must be considered, including supply-demand matching, agricultural machinery
performance parameters, fuel consumption, and time constraints. Agricultural machinery often
needs comprehensive information-gathering and scientific decision-making methods for field
collaborative management. In agricultural machinery operations, there is usually an asymmetry in
supply and demand information, and management authorities frequently need more scientifically
rational scheduling and management plans, along with efficient and sensible task allocation
strategies. Addressing these issues is essential in achieving successful multi-machine collaborative
operations in agricultural fields.
Therefore, it is necessary to study the agricultural machinery static task of agricultural
machinery. The innovations and contributions of this research are as follows: (1) This paper
proposes a path pre-planning model based on a simulated annealing algorithm and a static task
assignment model based on a genetic algorithm. (2) The tournament selection method can avoid
the problem of early convergence to the local optimal solution, keep the population's diversity, and
increase the algorithm's global search ability. (3) The adaptive crossover operator and adaptive
mutation operator are designed. The two-segment coding method is used to optimise the objective
function. A multi-crossover operator and multi-population mutation method are constructed to
improve population diversity and enhance population exploration's ability to achieve
multi-machine cooperative static task allocation. (4) To optimise the path further, a 2-opt local
optimisation mutation operator and an improved circle algorithm are used to optimise the path
better.
The rest of this paper is as follows: the second section introduces the cooperative operation

model, the third section presents the task assignment model, the fourth section designs the
algorithm, the fifth section provides the simulation results, and the sixth section discusses the
conclusion.
2. Problem formulation
Task allocation refers to the process of assigning feasible tasks to suitable performers. It
involves determining the nature, requirements, and priorities of jobs and giving them to a
ppropriate individuals or resources to ensure practical task completion, maximizing the ben
efits obtained when all tasks are accomplished. Multi-machine collaborative static task allo
cation in agricultural machinery refers to establishing a mapping relationship between agric
ultural machinery units and multiple sections of cultivated land. Subsequently, before com
mencing operations, the farm machinery allocates task assignments and their order to the
designated machinery units to maximize their benefits. Consequently, agricultural machinery
can operate systematically in cultivated fields, facilitating coordinated scheduling and man
aging multiple machinery units within a specific region.Using the set �� ={�1 ,�2 ,⋯, �� }repr
esents m operational agricultural machinery units.Using the set �� ={�1 , �2 , ⋯, �� } means n

tasks.The parameters of the i-th agricultural machinery are defined as follows �� =
{��� , �� , �� , �� , ��� , ��� , ��� },(i = 1,2, ⋯, m).Table 1 lists the main parameters adopted in this st
udy.
Table 1 the main parameters used in this study

Symbols

Description

vai

The average speed (km/h) of operation for the i-th agricultural machinery.

di

The working width (m) of the i-th agricultural machinery during operation.

wi

The average operational capacity of the i-th agricultural machinery in terms of area covered (m²/h).

vi
tti
cvi
cw i
dT j
IT j
Sj

The average speed (km/h) at which the i-th agricultural machinery travels in a non-operational
state.
The average time (h) taken for the i-th agricultural machinery to perform a turnaround during
operation.
The average fuel consumption (L/h) of the i-th agricultural machinery while traveling in a
non-operational state per unit of time.
The average fuel consumption (L/h) of the i-th agricultural machinery per unit of time during
operation.
The width of the vertical operation path for task �� .

The length of the parallel operation path for task �� .
The operational area of task �� .

For analysis, a section of farmland was selected in the farm testing field. This area was divided
into 15 idealized plots based on the requirements. Each parcel of farmland was considered an

obstacle, and free traversal was restricted due to the distribution of the farmland. The Ovitalmap
was utilized to establish the farmland model, and the model was visualized. In the model, white
indicates roads, and blue represents boundaries, as depicted in Fig 1.

Fig.1 Model of experimental farmland
2.1.The primary hypothesis of multi-machine cooperative operation
Due to the complexity of collaborative operations and to simplify the problem and facilitate
computation, the following basic assumptions are made based on standard operational scenarios:
① The performance parameters of agricultural machinery and the positional parameters of
farmland are known. Each plot of land is not connected to any other plot.② The number of tasks
must be greater than the number of farm machines.③ Each task plot is assigned to only one
agricultural machinery unit, with the route planning for each task plot known.④ Agricultural
machinery departs from the garage, completes all assigned tasks, and returns to the garage.⑤ The
farmland is obstacle-free. The agricultural machinery is in an ideal state.
2.2.Multi-machine cooperative operation model
(1) The cost of completing a task for an agricultural machinery unit is calculated as the
distance the machinery travels from the garage to the designated task location and back to the
garage. Each agricultural machinery unit's overall operational time and fuel consumption are
computed. In practical applications, agricultural machinery typically departs from the garage to
sequentially visit task areas, each being called only once. The machinery returns to the garage
after completing the final task. The cost associated with the path of each machinery unit is as
follows:
�� = ���� ,�� +
0

1

�� −1
�(��� , ���+1 ) + ���� ,��
�=1
�
0

(1)

�

�

Formula 1.Where �� represents the path cost of agricultural machinery i .Where ���0,��1 represents
the distance from the starting point �� to the first task point ��1 for agricultural machinery i .Where
DiTi ,si represents the distance from the last task point �� � to the return point ��0 for agricultural
ni 0

i

�

−1
machinery i .Where Tk=1
D(Tik , Tik+1 ) represents the total distance traveled by agricultural
�
machinery �1 from task e to ��� .The distance is calculated as shown in Formula (2).

D (T k ,T k + 1 ) =

(xk + 1 - xk )2 + (yk + 1 - yk )2

（2）

The objective function is established to minimize the total path cost for all agricultural machinery
units,and it is defined as follows:
minf总 = min(

�� = �，i Î M

M
(Disi ,Ti +
i=1
0 1

Ti −1
D(Tik , Tik+1 ) +DiTi ,si ))
k=1
i 0
n

（3）

（4）
Formula (3) represents the minimization of the total path cost between task areas,while Formula (4)
represents that all agricultural machinery units need to complete tasks in all task areas.
The fuel consumption �� comprises three parts: fuel consumption during travel,fuel consumption
for turning during operation,and fuel consumption during operation.This is illustrated in Formula
(5).
�

�� = � ∗ ��� +
��

�
�_����(��) ∗ �_�(�) ∗ ��� +
�=1

� ��
∗ ���
�=1 ��

(5)

In Formula (5),n_turn(ij) represents the number of U-turns for the i-th agricultural machinery at
the j-th task location.
(3)The total time �� to complete tasks consists of three components: machinery travel
time,machinery in-field turning time,and machinery operation time.This is represented by Formula
(6).
�

�� = � +
��

�
�_����(��) ∗ �_�(�)+
�=1

� ��
�=1 ��

(6)

3. Establishment and Process Design of Multi-Machinery Collaborative Task Allocation
Model
3.1.Framework for Task Allocation of Multiple Agricultural Machinery
The collaboration of various agricultural machinery can be divided into two categories: static
task allocation and dynamic task allocation. This article mainly focuses on the static task
allocation for multiple agricultural machinery working collaboratively, as illustrated in Fig.2.In
static task allocation, tasks are reasonably allocated to each agricultural machine, and an efficient
and rational global resource allocation plan is generated based on the known task information.

Fig.2 Overall framework of multi-computer cooperative task allocation relationship
3.2 Task Allocation Methods
�!(�−1)!
There are (�−1)!(�−�)!
possibilities to assign n tasks to m-machine in an orderly way.When n is

large,we can not use the exhaustive method to get the optimal task assignment.At this time,we
often use the heuristic method to get a feasible solution [24-25];in this paper,a simulated annealing
algorithm and a genetic algorithm are used to solve the problem.
3.2.1 Path Preplanning Based on Simulated Annealing Algorithm
Simulated Annealing is a global optimisation algorithm[26]used to find the optimal solution
to a problem within a search space. Inspired by solid-state annealing principles, it simulates a solid
object's cooling process from high to low temperature to explore the solution space. This paper
employs the Simulated Annealing algorithm for path preplanning to obtain a feasible solution with
the lowest cost. The specific process is outlined below:
(1) Set the initial value of the iteration count,initial temperature �� ,final temperature t,and the
length of the Markov chain.

(2) Initialize the current offspring population as route_new=route and set the initial distance
matrix and path.

(3) Sets the optimal path length to infinity and initializes the current and optimal paths to the
initial directions.
(4) When the temperature is greater than or equal to the last temperature, perform the following
steps:
① The number of iterated Markov chain lengths
② Perform path perturbation to generate a new path route.
③ Calculates the size of the new path.
④ If the length of the new way is less than the length of the current path, the length of the
current path is updated to the length of the new path.
⑤ Otherwise, the current new path is updated with a certain probability according to
Metropolis criteria. If the new path length is less than the optimal path length, the optimal path
and length are updated.
(5) Update the temperature.
(6) Finally, the optimal path and length are returned as the algorithm's output.
3.2.2.Task Allocation Based on Genetic Algorithm
Genetic Algorithm (GA) is a heuristic optimisation algorithm [27] inspired by the principles
of biological evolution and genetics in nature. It simulates the process of natural growth and has
strong global search capabilities, making it effective in finding better solutions in large search
spaces. Genetic algorithms typically involve three basic steps: selection, crossover, and mutation.
An adaptive crossover operator and a genetic algorithm with multiple adaptive modifications are
proposed. This algorithm employs two-stage encoding and uses tournament selection of
chromosomes, effectively addressing the problem of multi-machine collaborative task allocation.
4. Algorithm Design
4.1.Encoding
According to reference[28], a two-stage encoding method was employed, as illustrated in
Fig.3.The first part represents the task order, with n tasks represented by numbers from 1 to n,
utilising n digits. The second part denotes the number of tasks assigned to each agricultural
machine (AM) and consists of m digits. For instance, the encoding scheme is applied when n = 8
and m = 3.

Fig.3 Two-stage coding

4.2.Selection
Tournament selection is simple, effective, and easy to implement. It involves selecting a
small group of individuals to compete and selecting the fittest as the winner. This selection method
has a low computational cost and is suitable for large-scale problems and complex optimisation
tasks. Additionally, it aids in maintaining diversity; tournament selection allows weaker
individuals to participate in the competition, increasing the diversity of the selection process. Even
if an individual has relatively low fitness, he still has the chance to be selected, thus obtaining the
opportunity for survival and reproduction. This helps avoid the problem of early convergence to
local optima, maintains population diversity, and enhances the algorithm's global search capability.
Define the problem's fitness function, where higher-fitness chromosomes represent better
task allocation outcomes. The fitness function is defined as shown in Formula (7):
1
���� =
(7)
�
4.3 Adaptive Crossover Operator
(1) The sigmoid function is a commonly used logistic function, also called the logistic
function. It maps real numbers to the interval (0,1) and is frequently utilized to convert continuous
inputs into probability values. Its formula is given by Formula (8):

���� =

1

(8)

1+�−�

Where x is the input value,e is the base of the natural logarithm (approximately equal to 2.71828).
The output of the function is a value between 0 and 1.
(2) In Formula (10). Using the method of adaptive step size, we calculate a relative evolutionary
algebraic value according to the number of population (N) so that its range r, Formula (9) is shown.
The step size of R will increase with algebra, and the value will rise first and then decrease. This
scaling effect can be used to control the genetic algorithm's early exploring ability and later
balancing power; this makes evolution more exploratory in the early stages and more balanced in
the later stages so that fitness changes over a smaller range. The R trend is shown in Fig.4.
� = 2 ∗ ���(�) ∗
�=

1

1+���(−�)

∗

���

������

− ���(�)

(������−���+1)
������

(9)
(10)

Where n is the number of population, Gen is the number of current iterations, and MAXGEN is the
total number of iterations.

Fig.4 Trends in R
(3) Overshoot
�����ℎ��� =

(���(�� )−����(�� ))

(11)

����(�� )

In Formula (11),max(�� ) represents the maximum value of the path cost for agricultural machine
m(i),and Mean(�� ) represents the average path cost for all agricultural machines m.
��1 =
��2 =

(���(��1 )−����(��1 ))

(12)

(���(��2 )−����(��2 ))

(13)

����(��1 )
����(��2 )

In Formula (12)-(13),to1 and to2 represent the two individuals' overshoot.
(4) Definition of adaptive tolerance as shown in Formula (14): the crossover operator can be
dynamically adjusted, and in the global search phase, the population diversity can be increased by
increasing the crossover probability to explore the solution space better. In the local search phase,
the crossover probability can be reduced gradually, which makes the algorithm search the local
area near the excellent solution more centralized.
�� = ������ + � ∗

���∗(������ −������ )

(14)

������

Tolmin and Tolmax are two given thresholds representing the parameter's minimum and maximum
values, respectively. R is an adaptive step size to achieve dynamic adjustment and optimization of
parameters.
(5) Based on the new population resulting from the selection of the bidding tournament, two
chromosomes are randomly selected in the new population, and the crossover probability is
calculated separately for each chromosome. As shown in Formula (15) - (16).
��1 = ����� ∗ (�1_���� − �1_���) + �����
��2 = ����� ∗ (�2_���� − �2_���) + �����

�1_����−�1_���

(15)

�2_����−�2_���

(16)

�1_����−�1_���
�2_����−�2_���

Where Pcmax and Pcmin denote two given crossover probabilities,respectively,The average,
maximum,and minimum path costs of each agricultural machine among the m agricultural

machines in the first chromosome are represented by y1_mean,y1_min and y1_max.
The crossover probabilities of the two randomly selected chromosomes are normalised to obtain
the crossover probabilities. To ensure that each possibility is correctly considered and applied, the
problems associated with inconsistent probability distributions are avoided, thus better achieving
the desired effect of the optimisation algorithm. As shown in Formula 17-18.
��2 = ��1 ∗ �1 + ��2 ∗ �2
(17)
�1 + �2 =1
(18)
4.3.1Sequential intersections (OX)
The crossover process of the sequential crossover operator is shown in Fig.5 ① Selec
t two individuals (Dad and Mom) randomly.② Randomly select two crossover points (Cro
ssPoint1 and CrossPoint2),such that CrossPoint1 is smaller than CrossPoint2.e.g., CrossPoi
nt1=2, CrossPoint2=4.③ The mother's chromosome is passed as it is in the gene section
between CrossPoint1 and CrossPoint2.④ The remaining partial gene segments in Mom are
inserted into the remaining segments of the offspring (offspring) in the order in which th
ey appear in Dad. A random breakpoint is selected for the second part of the chromosom
e, and then the two gene segments are reversed in order.

Fig.5 Sequential crossover operator
4.3.2 Partially-Mapped Crossover (PMX)
The crossover process of the partially mapped crossover operator is shown in Fig.6. ① Two
chromosomes are randomly obtained from the selected population.② In the first part of the
chromosome, two random numbers are generated to satisfy 0≤k1<k2≤ n the length of the
chromosome, such as k1=2,k2=6, as the starting position of the intercepted chromosome
segments.③ The two intercepted segments are exchanged in position, and the new offspring can
be obtained.④ The final zygote chromosome can be obtained by filling it according to the
mapping relationship.⑤ In the second part of the chromosome, a random crossover point is
generated, and then the two gene segments are reversed.

Fig.6 Partial mapping crossover operator
The design process of the adaptive crossover operator is shown in Fig.7, which is
implemented as follows: ① Use the tournament selection method to get a new population to select
two chromosomes randomly; one is the parent generation, the other is the mother generation, the
number of newly generated individuals must be even, if it is odd will be converted to an even
number of individuals in a certain way.② The crossover probabilities Pc1 and Pc2 were calculated
for the paternal and maternal generations,respectively,and the total crossover probability Pc.③ The
random number�� ∈ [0,1],generated，If Rr<Pm,perform crossover.Then,assess the magnitudes of

tolerance (sp) and the parent's overshoot(tol).If to1<sp,apply ordered crossover (OX) operation;
otherwise,use partially-mapped crossover (PMX) operation.Apply the same logic to the maternal

parent.④ Remove the randomly selected chromosome from the population,then repeat the process
of step ③ With the remaining individuals by randomly selecting two individuals again.⑤
Generate a new population.

4.4.Mutation operator

Fig.7 Adaptive intersection operator

4.4.1.Exchange mutation operator
The process of exchanging variation operators is shown in Fig.8,① Select an individual (Dad)
randomly.② Two gene positions (Position 1 and Position 2) are randomly selected in the first part
of the chromosome. Their values are exchanged.③ A new individual (the offspring) is produced.
The exchanged genes are placed in the offspring.④ Generate two random crossover points in the
second part of the chromosome and exchange the gene fragments.

Fig.8 Exchange of variational operators
4.4.2 Insert Mutation Operator
Inserting the mutation operator is shown in Fig.9,① Randomly select an individual (Dad).②
Two gene positions (Position 1 and Position 2) are randomly selected in the first part of the
chromosome.The gene from Position 2 is inserted into the position before Position 1.③ A new
individual (offspring) is generated,and the inserted gene is placed in the offspring.④ Generate two
random crossover points in the second part of the chromosome for gene fragment insertion.

Fig.9 Insertion of mutation operator
4.4.3 The process of designing the adaptive mutation operator is illustrated in Fig.10, and its
implementation is as follows:① Calculate the similarity of each individual.② Calculate the
diversity of each individual.
��� = ���(���, 2)./(���_���� − 1)
(19)
In Formula 19, sim denotes the value of similarity, pop_size denotes the size of the population, and
div characterises the diversity of each individual.③ Adjust the mutation rate based on the fitness

value,as shown in Formula (20).
�� = (1 − ���) ∗ �� + ��� ∗ ���
(20)
Where pm represents the initial mutation probability, Pm indicates the adaptive mutation probability,
and fit represents the fitness value of each individual in the population.④ Perform mutation based
on the mutation rate. If Rr<Pm is satisfied, perform crossover. Randomly select a mutation method,
apply it to the i-th individual, and generate a new population.

Fig.10 Adaptive mutation operator
4.5.2-opt Optimization of local variation optimizer and Circle modification algorithm

(1) 2-opt belongs to the local search algorithm, which is an effective tool for solving combinatorial
optimisation problems. The algorithm is implemented by ① Randomly selecting 2 points, i and j,
in the chromosome produced after mutation.② The path before i is unchanged and added to the
new way; the path between i and j is flipped in its encoding and added to the new approach; and
the path after j is unchanged and added to the new way.③ The second part is the same.
The schematic diagram of the 2-opt algorithm is shown in Fig.11, which shows that the gene
grouping breakpoints in the first part are i = 2,j = 6, and the gene grouping breakpoints in the
second part are i = 1,j = 2.

Fig.11 2-opt locally optimized variational operator
(2) Modified circle algorithm is an optimization algorithm, thus making it better in every aspect
and can provide better performance, accuracy and adaptability. First, a Hamilton circle is obtained,
then the process is modified to get another Hamilton circle with lesser weights until it cannot be
improved, and then it stops. For 1≤i<i+1<j≤n,(2) Construct a new Hamilton circle, described as
shown in Fig.12.

Fig.12 Circle Modification Algorithm
4.6 Algorithmic flow
The flow of the designed algorithm in this paper is shown in Fig.13.
(1)Initialize the population according to the problem and use the SA algorithm for path
preplanning.

(2)Based on the new population generated by the SA algorithm, if a new population is generated,
then continue to use the genetic algorithm to randomize the task assignment for each individual;
otherwise, repeat step (2) until the last individual is executed.
(3) Select the better-adapted individual based on the tournament approach.
(4) According to the coding method, randomly select two individuals in the chosen population,
delete the randomly selected individuals, perform crossover based on the crossover method,
calculate the adaptation value of each individual to find the best individual, and then complete the
mutation operation on the new population based on the process of adaptive mutation until the new
population is generated, calculate the adaptation value of each individual, and compare the
optimal produced by crossover and mutation fitness values to find the optimal solution.
(5) Optimize the optimal solution using 2-opt and modified complete circle algorithms to obtain
the new optimal individual. If the current number of iterations (gen) is less than the maximum
number of iterations (MAXGEN), repeat steps (3)-(5).
(6) If the number of iterations is reached, the individual with the highest fitness of the current
population is selected as the solution for this task assignment.

Fig.13 Flow of the algorithm
5 Algorithm Simulation and Data Analysis
5.1 Optimization Performance Testing of Hybrid Algorithms
In the simulation experiments based on hybrid algorithms, to validate the effectiveness of the
proposed approach, several hundred simulation experiments were conducted using MATLAB
R2020b on a computer with an Intel(R) Core(TM) i7-8750H CPU running at 2.20 GHz and 8GB
RAM.

Detail settings: Initial temperature t=120, final temperature �� =1, the number of populations

N=200, Markov chain length is set to 100; the maximum number of iterations MAXGEN is set to
2000, the initial crossover probabilities of ����� ,��� ,����� are 0.4, 0.55, 0.85, respectively, the
�� initial variance probability is 0.1. The tolmax,tolmin are set to 0.8, 0.05.
5.2 MTSP experimental comparison

In this experiment, we conducted a series of trials on multitasking task allocation, covering
algorithms such as IPGA and GA2PC [29], GA, GAG, HCGA and SAGA[30-31], GA-PMX,
GA-OX and GA-CX[32], as well as the improved genetic hybrid optimization algorithm that we
proposed. To evaluate the performance of the hybrid algorithms and our approach, we use multiple
datasets publicly available in TSPLIB, including eil51, eil76, eil101, kroA100, kroA150, kroA200,
att48, lin318, rat575, pr1002, U1432, vm1748, pcb3038, etc. On different datasets, we conducted
several experiments and calculated the average values to derive the average distance cost, and the
relevant data are shown in Tables 2,3, 4 and 5. Compared with other methods, our improved
genetic hybrid optimization algorithm performs well. It is the best performer regarding the total
distance metric, which can effectively reduce the path cost. These results further demonstrate the
superior performance of our improved genetic hybrid optimization algorithm in the multitasking
task allocation problem.
Table 2 Comparison of distance cost between IPGA,GA2PC and improved genetic hybrid
optimization algorithms
No.

case

m

IPGA

GA2PC

IGHOA

1

Eil51

3

478

543

471.77

2
3

KroA100

4
5

KroA150

6

5

549

586

506.13

3

24288

26653

25041.00

5

30710

30408

31147.00

3

35428

47418

33606.00

5

43725

49947

39063.00

Table 3 Comparison of distance cost of GA,GAG,HCGA,SAGA and improved genetic hybrid
optimization algorithm
No.

case

m

GA

GAG

HCGA

SAGA

IGHOA

1

Eil51

3

657.97

509.99

476.30

472.56

471.77

2

4

569.20

549.20

522.97

503.34

487.28

3

5

624.18

608.55

581.89

567.32

506.13

3

980.54

666.80

661.20

653.96

610.98

5

4

849.18

695.06

694.64

690.94

635.35

6

5

1018.18

780.27

771.50

747.34

627.57

7

6

862.45

825.35

804.21

800.84

642.42

4

1092.61

817.89

803.38

796.96

772.50

9

5

1137.01

847.48

857.54

867.24

770.23

10

6

1099.08

75.62

900.34

900.90

803.34

11

7

1062.69

900.97

898.77

900.72

803.11

4

8

Eil76

Eil101

Table 4 Comparison of distance cost of GA,HCGA and and improved genetic hybrid optimization
algorithms
No.

case

m

GA

HCGA

IGHOA

1

Eil101

4

921.2

813.0

772.50

2

Lin318

4

135188.2

71646.4

49237.60

3

Rat575

4

33008.9

13057.0

8541.41

4

Pr1002

3

3218723.7

721022.8

305517.00

5

Pr1002

6

1524822.4

538609.8

317816.00

6

U1432

3

2072059.0

483942.8

170505.00

7

U1432

6

914170.0

308176.0

171523.00

8

Vm1748

3

7719677.9

1858539.5

609624.00

9

Vm1748

6

3365320.0

938670.90

697024.00

10

Pcb3038

3

3699627.9

1302418.6

163582.00

11

Pcb3038

4

1837962.6

657501.3

163248.00

12

Pcb3038

6

1497143.3

427950.6

165281.20

Table 5 Comparison of distance cost of GA-PMX,GA-OX,GA-CX and improved genetic hybrid
optimization algorithms
No.

case

m

GA-PMX

GA-OX

GA-CX

IGHOA

1

Att48

2

52343.48

52023.49

52773.84

37752.60

2

4

64954.87

66324.27

64803.34

37514.20

3

6

75357.03

78344.59

77401.42

40504.60

4

8

93423.03

96930.30

94066.53

44422.40

2

32145.24

32872.40

32423.66

24948.00

6

4

46748.49

48820.87

47549.87

29006.00

7

6

57152.93

59349.57

56772.45

26652.00

8

58265.54

65924.12

62509.56

28524.70

2

43113.54

43381.04

42835.79

32203.00

10

4

59332.85

61113.17

61185.34

36903.00

11

6

71069.14

74566.69

72132.12

35202.00

12

8

81819.18

86174.12

84449.72

35568.70

2

48368.55

46622.32

48537.27

36763.30

14

4

66758.95

67152.20

69299.25

36669.10

15

6

82791.72

82620.29

84913.85

38508.00

16

8

95258.01

97601.72

99075.72

39036.50

5

KroA100

8
9

13

KroA150

KroA200

5.3 Simulation and Analysis
To verify the effectiveness of the hybrid algorithm in task allocation, we designed a set of
simulation experiments involving task-area allocation. In the experiments, we used different
numbers of farm machines (3, 5 and 6) for task allocation. We used the performance parameters of
each of the three farm machines according to the data provided in the reference[20]. The
performance parameters of the farm machines are shown in Table 6, and the total number of tasks
is 16, with the main parameters of each job shown in Table 7. These task fields are relatively
regular rectangular fields. We evaluate the effectiveness of the improved genetic hybrid algorithm
by comparing the performance of the traditional and enhanced genetic hybrid algorithms on the

static task allocation problem. Through these experiments, we aim to verify whether the improved
hybrid algorithm can better solve the task allocation problem to improve the efficiency of
farmland operation and maximise the overall benefits.
Table 6 Performance parameters of agricultural machinery
Agricultural
machine
serial
number

Operating
width/m

Operating
capability/(
m2/h)

Road
speed/(k
m/h)

Fuel
consumption in
operating
condition/(L/h)

Non-operating
fuelconsumptio
n/(L/h)

Turnaround
time/h

1

6.9

7000

10

7

3.0

0.004

2

5.5

5000

10

5

2.5

0.003

3

3.7

4000

10

4

2.0

0.002

Table 7 Parameters of the mission field
Task number

Lengths/m

Widths/m

Area /m2

1

70

127

8890

2

62

138

8556

3

101

146

14746

4

67

146

9782

5

63

139

8757

6

130

150

19500

7

72

125

9000

8

73

149

10877

9

72

138

9936

10

54

103

5562

11

98

160

15680

12

56

106

5936

13

118

153

18054

14

135

100

13500

15

74

144

10656

16

65

134

8710

According to the analyzed results in Tables 8,9 and 10, it can be learned that the static task
allocation based on the improved genetic hybrid algorithm presents a significant advantage for the
same number of tasks. Compared with the traditional genetic algorithm, the method reduced the
fleet path cost by about 31.22%,31.0%, and 21.4%, respectively. In addition, the time cost
decreased by 18.68%,19.40% and 13.74%. Notably, there was no significant increase in fuel
consumption as the number of farm machines increased. The experimental results clearly show
that the static task allocation method based on the improved genetic hybrid algorithm performs
better when the number of tasks remains constant.
To verify the reasonableness of the algorithm's cost reduction, a series of experiments were
conducted on the traditional genetic algorithm and the improved genetic hybrid algorithm in the
case of task allocation using 4,5 and 6 farm machines. Each set of experiments was repeated 10
times and averaged to obtain data on average distance cost, average fuel consumption and average
time spent; the results are shown in Fig.14, Fig.15 and Fig.16.With the same number of iterations
and tasks, the experimental results show that the static task allocation results based on the
improved genetic hybrid algorithm can be seen to be about 32.34%,28.10% and 21.54% lower on
average in terms of swarm path cost compared to those based on the traditional genetic algorithm;

the average fuel consumption is reduced by 0.195%,0.156% and 0.074%, respectively; and the
average time spent is by 9.83%,10.82% and 13.02 %. These data indicate that the static task
allocation method using the improved genetic hybrid algorithm is more effective when the number
of tasks remains constant. The simulation results further show that using the improved genetic
hybrid algorithm can obtain better task allocation results while reducing the distance and time
travelled by the agricultural machine. Using the enhanced genetic hybrid algorithm for task
allocation can significantly reduce the farm machine's burden while preventing the agricultural
machine from making unnecessary travelling paths. Therefore, the static task allocation method
based on the improved genetic hybrid algorithm is advantageous. These results further validate the
effectiveness of our algorithm in reducing cost and optimizing resource utilization.

Table 8 Results of tasking of 4 agricultural machines
Serial No.

Methods

AM 1

AM 2

AM 3

AM 4

1

1

�� /�

�� /�

�� /ℎ

2

6461.30

181.81

35.61

14

4444.20

181.64

28.96

14→6→9→10→7
1

GA

12→13

11→8→4→15→3→
16→5

2

IGHOA

16→13→8→4→11

5→10→7

3→15→2→9→6→12

Table 9 Results of tasking of 5 agricultural machines
Serial No.

Methods

AM 1

AM 2

AM 3

1

GA

14

13

1

2

IGHOA

12

1

14

AM 4

AM 5

9→4→11→7→6
5→16→10→2
16→13

12→8→3→15
9→2→6→7→15
3→11→4→10→5

�� /�

�� /�

�� /ℎ

7206.40

181.65

39.13

4972.70

181.69

31.54

Table 10 Results of tasking of 6 agricultural machines
Serial

Methods

AM 1

AM 2

AM 3

AM 4

AM 5

1

GA

14

1

7

16→13

6

2

IGHOA

14

1

12

6→9→2

No.

5→10→7→15→3
11→4→8→13

AM 6
9→12→5→10→4
8→15→2→11→3
16

�� /�

�� /�

�� /ℎ

7502.2

181.59

40.2952

5897.3

181.59

34.7590

Fig.14 Translation of average distances for different farm machine task assignments

Fig 15 Average fuel consumption for different farm machine task assignments

Fig 16 Average time for different farm machinery task assignments

5.4 Simulation Experiment on Real-Field Tasks
To validate the effectiveness of the proposed task allocation approach, we conducted
algorithmic simulations using real-world farmland coordinates expressed in latitude and longitude.
Fig 1 depicts the distribution of operational tasks within Chang ji Huaxing Farm, where 15 duties
were assigned using 3 and 6 farm machines. The specific task parameters are detailed in Table 11,
sourced from modelling data provided by Ovitalmap.Through this simulation experiment, we can
more precisely assess the efficacy of the proposed task allocation method in natural farmland
settings. This not only enhances the reliability of the investigation but also provides us with a
more authentic data-set to validate the algorithm's effectiveness.
Table 11 Parameters of the mission field
Task number

Widths/m

Lengths/m

Area/m2

1

241

178

42898

2

277

172

47644

3

216

166

35856

4

214

160

34240

5

234

188

43992

6

275

183

50325

7

212

177

37524

8

218

174

37932

9

233

153

35649

10

273

153

41769

11

207

153

31671

12

219

153

33507

13

307

173

53111

14

302

172

51944

15

316

157

49612

（a）

（b）
Fig.17 Simulation results of the proposed method in agricultural fields: (a) 3 Agricultural
machines;(b)6 Agricultural machines
The simulation was validated using the farmland's actual latitude and longitude coordinates. We
conducted simulation experiments using three and six farm machines, respectively and obtained
the results shown in Fig.17.The results show that the method effectively solves the path planning
problem used for multiple farm machines.
6 Conclusion
This article presents a global path planning and task allocation algorithm. Firstly, we
investigated the problem of static task allocation for collaborative multi-agricultural machinery
operations. We constructed a model that combines pre-planned paths with static task allocation.
Secondly, we introduced logical functions and overshoot and established an adaptive tolerance
mechanism that dynamically adjusts crossover operators. In the global search phase, we designed
adaptive crossover and adaptive mutation operators to improve the genetic algorithm, enhance
population diversity, and better explore the solution space. This approach improves diversity
within the population, enabling it to search for new solutions in the search space.
Additionally, we employed the 2-opt local optimization mutation operator and Modified
circle algorithm. These methods draw inspiration from local search principles, altering the order of
paths or nodes to discover more optimal solutions, playing a crucial role in various optimization
algorithms. Finally, we validated the performance of the proposed algorithm using publicly
available datasets from TSPLIB. Compared to other methods, we verified the effectiveness of this
approach, as it significantly reduces path costs. However, it's important to note that this paper did
not consider factors such as obstacles, road conditions, and task allocation fairness in the
algorithm. In future work, we will address these issues, including path planning with barriers, road
conditions, and balanced task allocation. We will also research how to handle the influence of
unknown obstacles on path planning.
CRediT authorship contribution statement
Haohao Du: Methodology, Validation, Writing - original draft. Huicheng Lai: Writing - review
& editing. Guxue Gao: review & editing. Xiaopeng Wen: review & editing. Yifei Li: review &

editing. Haidong Wang: review & editing. Guo Zhang.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal
relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This study is supported by the National Key R&D Program of China (Grant Nos.
2022ZD0115803).

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